Question

2
The ratio of the present ages of A and B is 3:4. Five years hence, the ratio of their ages will be
4:5. Find their present ages.​

Answer 1

Given :

• The ratio of the present ages of A and B is 3:4.
• Five years hence, the ratio of their ages will be 4:5.

To find :

• Their present ages.

Solution :

Consider,

• Present age of A = 3x years
• Present age of B = 4x years

After 5 years,

• Age of A = (3x+5) years
• Age of B = (4x+5) years

According to the question:-

• Five years hence, the ratio of their ages will be 4:5.

$\implies\sf{(3x+5):(4x+5)=4:5}$

$\implies\sf{\dfrac{3x+5}{4x+5}=\dfrac{4}{5}}$

$\implies\sf{16x+20=15x+25}$

$\implies\sf{16x-15x=25-20}$

$\implies\sf{x=5}$

• Present age of A = 3×5 = 15 years

• Present age of B = 4×5 = 20 years

Therefore, the present age of A is 15 years and the present age of B is 20 years.

Answer 2

Answer:

Let the present age of A and B be 3x and 4x years respectively.

After five years, age of A = 3x + 5 years

After five years, age of B = 4x + 5 years

Therefore, the ratio of their ages after five years

= 3x + 5

4x + 5

This is given to be 4:5

Therefore, 3x + 5 = 4

4x + 5 = 5

Cross multiplication gives

5 (3x+5) = 4 (4x+5)

or, 15x + 25 = 16x + 20

or, 15x - 16x = 20 - 25

or, - x = -5

x = 5

Therefore, present age of A = 3x

= 3 × 5 = 15 years

present age of B = 4x = 4×5 = 20 years .